For the weak Mott regime, magnetic order may not exist even in the layer polarized limit[1]}. In the single moiré layer based on MoTe\(_2\) /WSe\(_2\) , the weak Mott insulator was shown to be more consistent with a U(1) spin liquid phase with spinon Fermi surface[1]} given the large spin susceptibility at lowest temperature. Smoking gun evidence for such a neutral fermi surface has remained elusive because of the lack of the probe of neutral excitations. We propose to add a monolayer TMD separated from MoTe\(_2\) /WSe\(_2\)  by a hBN similar to the setup of Ref. gu2021dipolar,zhang2021correlated. If the layer polarized limit is indeed a spinon Fermi surface state, then we should use the four-flavor Abrikosov fermion \(f_{i;a\sigma }\)  to attack the four-flavor spin model. In the \(x=0\)  limit, the band for \(f_{i;t\sigma }\)  is empty while \(f_{i;b\sigma }\)  forms the spinon Fermi surface. Upon increasing \(x\) , there is a one component to two components Lifshitz transition and we reach a U(1) spin liquid phase where both layers host a spinon Fermi surface. Physically \(f_{t;\sigma }\)  can be interpreted as a fermionic exciton formed by binding electron \(c_{i;t\sigma }^\dagger \)  with a holon in the bottom layer. This phase will support metallic counter-flow transport \(\rho _{\text{counterflow}}(T) \sim T^{\alpha }\)  with some non-Fermi-Liquid (NFL) exponent \(\alpha \)  due to gauge fluctuation. The exact value of \(\alpha \)  is still not well established theoretically[3]}, [4]}, [5]}, [6]}, [7]} and we hope the future experiment in moiré bilayer could provide experimental constraint on the theory of spinon Fermi surface phase in 2+1d. The neutral Fermi surface could also be revealed by Friedel oscillation in terms of the layer polarization, which may be measured electrically.
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